Prime Factorization is a mathematical method utilized to split up a composite number into its prime factors. Composite numbers could be divided by more than just 1 and itself to result in a whole number. Prime numbers can only be divided by 1 and themselves, for example 2, 3, 5, and 7.
By working out the prime factors of a number, we can streamline fractions and equations, as well as understand the properties of that number. Let’s get a closer look.
Methods for Figuring out Prime Factorization
There are two major methods for figuring out prime factorization. You can employ a factor tree, or you could factor by dividing by prime numbers. One as well as the other processes will yield you the exact outcome.
Factor Tree Method
The initial method is using a factor tree. To make a factor tree:
Start by noting the number you are attempting to factor at the top of the page.
Under it, create branches for the factors.
Proceed by creating branches and factoring before you reach a prime number.
Here’s an instance of the thinking process:
We recognize that 6 * 6 = 36.
Is 6 a prime number? No. 2 * 3 = 6.
Are 2 and 3 prime numbers? Yes. We have reached the end.
The prime factorization of 36 will be 2 x 2 x 3 x 3. To envision this process, we could create a factor tree for 36 as ensues.
As demonstrated, the prime factorization of 36 is found by multiplying the prime factors at the bottom of the tree, which are 2 * 3 * 2 * 3.
Division Method
The next way for figuring out the prime factorization of a number is to begin utilizing a record of prime numbers. Write down the value you are attempting to factor. Then, divide the value by a prime number which divides evenly into it. It’s most convenient to start with the first few prime numbers, like 2, 3, and 5.
Let’s use the division method for prime factorization of 36.
What is a prime number that divides into 36? 2 → 2 * 18 = 36
Is 18 a prime number? No.
What is a prime number which divides into 18? 2 → 2 * 9 = 18
Is 9 a prime number? No.
What is a prime number which divides into 9? 3 → 3 * 3 = 9
Is 3 a prime number? Yes. We are done.
The prime factorization of 36 is 2 * 2 * 3 * 3, and here’s a depiction.
Utilizing both process, we found the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Despite the fact that we’ve already worked through a few examples, let’s do another one employing both methods.
Let’s utilize a factor tree to work out the prime factorization of 100.
We learned that 4 * 25 = 100.
2 * 2 = 4, and 2 is a prime number. 5 * 5 = 25, and 5 is a prime number. We are done.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Let’s try the division process:
What is the prime factorization for 100?
What is a prime number which divides into 100? 2 * 50 = 100
Is 50 a prime number? Nope.
What is a prime number which divides into 50? 2 * 25 = 50
Is 25 a prime number? Nope.
What is a prime number which divides into 25? 5 * 5 = 25
Is 5 a prime number? Yes. We are clear.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Uses of Prime Factorization
Prime factorization has many practical uses in mathematics. One of the primary uses is streamlining fractions. By working out the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and clarify the fraction.
For example, the fraction 8/24 could be streamlined by working out the prime factorization of both values. 8 = 2 * 2 * 2 and 24 = 2 * 2 * 2 * 3. By ruling out the common prime factor of 2, we are left with the simplified fraction of 1/3.
To see how this works, let's employ prime factorization to simplify the fraction 8/24. Foremost, work on prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Next, we cancel out ever common prime factors among the numerator and denominator.
8/24 = 2 * 2 * 2 / 2 * 2 * 2 * 3 = 1/3
After canceling out the common prime factors of 2, we are left with the simplified fraction of 1/3.
Prime factorization further executes an essential part in cryptography and computer science. As you proceed in advanced mathematics and science concepts, you will figure out more utilizations for prime factorization and be delighted you are a pro.
It’s Prime Time to Enhance Your Mathematical Abilities
Prime factorization is an essential theory in mathematics which allows us to streamline equations and fractions, as well as get a grasp of the properties of a value. By practicing and understanding the processes and uses of prime factorization, we can enhance our mathematical skills and analytical skills.
If you require support conquering prime factorization, contemplate reaching out to Grade Potential tutoring for expert support. Grade Potential teachers are experienced and educated in mathematics. They could provide customized learning and support to support you comprehend and apply prime factorization in your studies.
With the support of Grade Potential tutoring, you can improve your mathematical abilities, boost your confidence, and attain your academic aims.
